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A Mathematical History of Division in Extreme and Mean Ratio.

Author: Roger Herz-Fischler
Publisher: Waterloo : Wilfrid Laurier University Press, 2000.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Herz-Fischler, Roger.
A Mathematical History of Division in Extreme and Mean Ratio.
Waterloo : Wilfrid Laurier University Press, ©2000
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Roger Herz-Fischler
ISBN: 9780889207776 0889207771
OCLC Number: 923081853
Notes: ""Section 13. Miscellaneous Theories""
Description: 1 online resource (208 pages)
Contents: ""TABLE OF CONTENTS""; ""PREFACE""; ""A GUIDE FOR READERS""; ""A. Internal Organization""; ""B. Bibliographical Details""; ""C. Abbreviations""; ""D. Symbols""; ""E. Dates""; ""F. Quotations from Primary Sources""; ""INTRODUCTION""; ""CHAPTER I. THE EUCLIDEAN TEXT""; ""Section 1. The Text""; ""Section 2. An Examination of the Euclidean Text""; ""A. Preliminary Observations""; ""B. A Proposal Concerning the Origin of DEMR""; ""C. Theorem XIII,8""; ""D. Theorems XIII,1-5""; ""E. Stages in the Development of DEMR in Book XIII""; ""CHAPTER II. MATHEMATICAL TOPICS"" ""Section 3. Complements and the Gnomon""""Section 4. Transformation of Areas""; ""Section 5. Geometrical Algebra, Application of Areas, and Solutions of Equations""; ""A. Geometrical Algebra�Level 1""; ""B. Geometrical Algebra�Level 2""; ""C. Application of Areas�Level 3""; ""D. Historical References""; ""E. Setting Out the Debate""; ""F. Other Interpretations in Terms of Equations""; ""G. Problems in Interpretation""; ""H. Division of Figures""; ""I. Theorems VI,28,29 vs II,5,6""; ""J. Euclid's Data""; ""K. Theorem II,11""; ""L. II,11�Application of Areas, Various Views"" ""Section 6. Side and Diagonal Numbers""""Section 7. Incommensurability""; ""Section 8. The Euclidean Algorithm, Anthyphairesis, and Continued Fractions""; ""CHAPTER III. EXAMPLES OF THE PENTAGON, PENTAGRAM, AND DODECAHEDRON BEFORE �400""; ""Section 9. Examples before Pythagoras (before c. �550)""; ""A. Prehistoric Egypt""; ""B. Prehistoric Mesopotamia""; ""C. Sumerian and Akkadian Cuneiform Ideograms""; ""D. A Babylonian Approximation for the Area of the Pentagon""; ""E. Palestine""; ""Section 10. From Pythagoras until �400"" ""A. Vases from Greece and its Italian Colonies, Etruria (Italy)""""B. Shield Devices on Vases""; ""C. Coins""; ""D. Dodecahedra""; ""E. Additional Material""; ""Conclusions""; ""CHAPTER IV. THE PYTHAGOREANS""; ""i. Pythagoras""; ""ii. Hippasus""; ""iii. Hippocrates of Chios""; ""iv. Theodorus of Cyrene""; ""v. Archytas""; ""Section 11. Ancient References to the Pythagoreans""; ""A. The Pentagram as a Symbol of the Pythagoreans""; ""B. The Pythagoreans and the Construction of the Dodecahedron""; ""C. Other References to the Pythagoreans"" ""Section 12. Theories Linking DEMR with the Pythagoreans""""i. The Pentagram""; ""ii. Scholia Assigning Book IV to the Pythagoreans""; ""iii. Equations and Application of Areas""; ""iv. The Dodecahedron""; ""v. A Marked Straight-Edge Construction of the Pentagon""; ""vi. A Gnomon Theory""; ""vii. Allman's Theory: The Discovery of Incommensurability""; ""viii. Fritz�Junge Theory: The Discovery of Incommensurability""; ""ix. Heller's Theory: The Discovery of DEMR""; ""x. Neuenschwander's Analysis""; ""xi. Stapleton""; ""CHAPTER V. MISCELLANEOUS THEORIES""

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